Subgroups — #13129847

Order 1664.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718746	C₂	1	1	yes	maximal, characteristic
2	#11718233	C₂	1	2	yes	maximal, complemented
3	C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
4	C₂×#6106	—	2	2	no	—
5	#88128	C₄	1	1	yes	characteristic
6	#88106	—	2	2	no	—
7	C₄×#1055	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₁₃	—	2	1	no	—
9	C₂×D₅₂	—	2	1	no	—
10	C₂×D₅₂	—	4	1	no	—
11	C₁₃×C₄⋊C₄	—	4	1	no	—
12	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
13	#6106	—	4	2	no	—
14	#6106	—	4	2	no	—
15	C₂×#1055	D₄	1	2	yes	—
16	#6092	—	4	2	no	—
17	#1359	—	13	1	no	maximal, Sylow
18	C₂²×D₁₃	—	4	1	no	—
19	Q₈×C₁₃	—	4	2	no	—
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	4	1	no	—
22	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	D₅₂	—	4	2	no	—
24	D₅₂	—	8	2	no	—
25	#1055	D₈	1	2	yes	—
26	#1055	SD₁₆	1	2	yes	—
27	#492	—	13	1	no	—
28	#364	—	13	2	no	—
29	C₂²×C₁₃	#100	1	1	yes	characteristic
30	C₂×D₁₃	—	8	2	no	—
31	C₂×D₁₃	—	8	1	no	—
32	C₄×C₁₃	—	2	2	no	—
33	C₄×C₁₃	—	8	1	no	—
34	C₄×C₁₃	#102	1	2	yes	—
35	C₂×SD₁₆	—	26	2	no	—
36	C₄⋊Q₈	#261	1	1	yes	characteristic
37	#127	—	13	1	no	—
38	M₃₂	—	26	2	no	—
39	C₄×C₈	—	13	1	no	—
40	C₂×C₁₃	—	2	1	no	—
41	C₂×C₁₃	#331	1	1	yes	characteristic
42	D₁₃	—	16	1	no	—
43	C₂×Q₈	—	2	1	no	—
44	C₂×D₄	—	26	1	no	—
45	C₂×D₄	—	52	1	no	—
46	SD₁₆	—	52	2	no	—
47	SD₁₆	—	52	2	no	—
48	C₂×C₈	—	13	2	no	—
49	C₄⋊C₄	—	4	1	no	—
50	C₄²	C₂×#261	1	1	yes	characteristic
51	C₁₆	—	52	2	no	—
52	C₁₃	#1359	1	1	yes	characteristic, complemented, Sylow
53	C₂³	—	52	1	no	—
54	Q₈	—	4	2	no	—
55	D₄	—	52	2	no	—
56	D₄	—	104	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
60	C₈	—	13	2	no	—
61	C₈	—	13	2	no	—
62	C₂²	—	104	2	no	—
63	C₂²	—	104	1	no	—
64	C₂²	#88121	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	8	1	no	—
67	C₄	#88115	1	2	yes	—
68	C₂	—	2	1	no	—
69	C₂	—	208	1	no	—
70	C₂	#11718297	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718297
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄²	C₂×#261
Fitting	C₁₃×C₄⋊Q₈	C₄
socle	C₂×C₁₃	#331
prime radical	#88128	C₄
cosocle	C₄×#1055	C₂²
hypercenter	C₄⋊Q₈	#261
hypocenter	C₁₃	#1359
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #11718233	C₂	semidirect
52. C₁₃	#1359	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11718746	2
#11718233	2
#1359	13